Complex industrial systems such as, for example, power generation systems and chemical, pharmaceutical and refining processing systems, have experienced a need to operate ever more efficiently in order to remain competitive. This need has resulted in the development and deployment of process modeling systems. These modeling systems are used to construct a process model, or flowsheet, of an entire processing plant using equipment or component models provided by the modeling system. These process models are used to design and evaluate new processes, redesign and retrofit existing process plants, and optimize the operation of existing process plants.
Simulation of complex industrial systems has been effected by using empirical models representative of the physical characteristics of such systems to identify and understand the factors contributing to behavior of the system. Any system that can be quantitatively described using equations and rules can be simulated. Dynamic process simulation generally involves simulating the performance of a proposed or existing plant or industrial process characterized by a performance that changes over time. One objective in modeling such a system is to understand the way in which it is likely to change so that the behavior of the system may be predicted and ways of improving the behavior through design or control modifications may be identified.
Dynamic process simulation typically involves performing calculations using numerous thermodynamic calculations, which can be extremely computationally intensive. One technique which has been employed in an effort to reduce the computational burden associated with calculation of thermodynamic functions centers around substituting an approximation for the functions. One such approximation, known as a Taylor series expansion, permits the extrapolation of a function given a reference point and independent variable sensitivity about that point. Considering a function ƒ(x) having continuous derivatives up to order (n+1), expansion of ƒ(x) in the form of a Taylor series is as follows:
                              f          ⁡                      (            x            )                          =                              f            ⁡                          (              a              )                                +                                                    f                ′                            ⁡                              (                a                )                                      ⁢                          (                              x                -                a                            )                                +                                                                      f                  ″                                ⁡                                  (                  a                  )                                            ⁢                                                (                                      x                    -                    a                                    )                                2                                                    2              !                                +          …          ⁢                                          +                                                                      f                                      (                    n                    )                                                  ⁡                                  (                  a                  )                                            ⁢                                                (                                      x                    -                    a                                    )                                n                                                    n              !                                +                      R            n                                              (        1        )            
In the past, Taylor series expansions have been used to characterize a discrete thermophysical property (e.g., density or enthalpy) within a simulation environment so as to form a “local model”. In general, such a local model is applicable only within the immediate vicinity of a reference point at which the condition of the property is assumed to be known. Updating of such local models conventionally occurs at a frequency based upon a confidence delta threshold associated with the independent model parameters (i.e., temperature, pressure, and composition). One drawback of this approach is that the independence of temperature, pressure, and composition relative to the property model of interest tends to force unnecessary updates of the model in the case of linear properties. On the other hand, this approach also often results in updates being performed with insufficient frequency in cases of highly non-linear properties.
Local models have been used in conjunction with flash algorithms for the purpose of evaluating thermophysical properties within simulation environments. However, it has been required to solve the complex thermodynamic equilibrium and specification equations of the flash algorithms in addition to evaluating such local models, which tends to also require consumption of substantial computing resources.